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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Non-interlaced solutions of 2-dimensional systems of linear ordinary differential equations


Authors: O. Le Gal, F. Sanz and P. Speissegger
Journal: Proc. Amer. Math. Soc. 141 (2013), 2429-2438
MSC (2010): Primary 34C08, 03C64
Published electronically: March 28, 2013
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Abstract: We consider a $ 2$-dimensional system of linear ordinary differential equations whose coefficients are definable in an o-minimal structure $ \mathcal {R}$. We prove that either every pair of solutions at 0 of the system is interlaced or the expansion of $ \mathcal {R}$ by all solutions at 0 of the system is o-minimal. We also show that if the coefficients of the system have a Taylor development of sufficiently large finite order, then the question of which of the two cases holds can be effectively determined in terms of the coefficients of this Taylor development.


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Additional Information

O. Le Gal
Affiliation: Laboratoire de Mathématiques, Bâtiment Chablais, Campus Scientifique, Université de Savoie, 73376 Le Bourget-du-Lac Cedex, France
Email: olegal@agt.uva.es

F. Sanz
Affiliation: Departamento de Álgebra, Geometría y Topología, Facultad de Ciencias, Universidad de Valladolid, Prado de la Magdalena, s/n, E-47005 Valladolid, Spain
Email: fsanz@agt.uva.es

P. Speissegger
Affiliation: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada
Email: speisseg@math.mcmaster.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11614-X
PII: S 0002-9939(2013)11614-X
Keywords: Ordinary differential equations, o-minimal structures
Received by editor(s): October 21, 2011
Published electronically: March 28, 2013
Communicated by: James E. Colliander
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.